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In scenarios of physical interest in Loop Quantum Cosmology, with apreinflationary epoch where the kinetic energy of the inflaton dominates, theanalytic study of the dynamics of the primordial fluctuations has been carriedout by neglecting the inflaton potential in those stages of the evolution. Inthis work we develop approximations to investigate the influence of thepotential as the period of kinetic dominance gives way to the inflationaryregime, treating the potential as a perturbation. Specifically, we study howthe potential modifies the effective mass that dictates the dynamics of thescalar perturbations in the preinflationary epochs, within the framework of theso-called hybrid prescription for Loop Quantum Cosmology. Moreover, we motivateand model a transition period that connects the kinetically dominated regimewith inflation, allowing us to study the interval of times where thecontribution of the potential is no longer negligible but an inflationarydescription is not yet valid. Finally, we include the main modifications comingfrom a slow-roll correction to a purely de Sitter evolution of theperturbations during inflation. We analytically solve the dynamics of theperturbations in each of these different epochs of cosmological evolution,starting from initial conditions fixed by the criterion of asymptoticHamiltonian diagonalization. This enables us to compute and quantitativelyanalyze the primordial power spectrum in a specific case, using a quadraticinflaton potential.

Effects of the inflaton potential on the primordial power spectrum in Loop Quantum Cosmology scenarios